1. Field of the Invention
The present invention is related to sigma delta modulators, and more particularly to delta-sigma modulators with improved stability at full range.
2. Related Art
Analog to Digital Converters (ADCs) are well known in the art for converting an analog input voltage into a digital output signal as a number of bits. Normally there is a linear correlation between an input voltage and a digital output value.
So-called Delta-Sigma ADCs are known in the art, which use an oversampling approach to convert the input analog signal, using integrators, comparators and digital filters, into a digital output signal. Description of this type of ADC and some embodiments can be found, e.g., in “Delta-Sigma Data Converters: Theory, Design, and Simulation,” by Steven R. Norsworthy (1996).
The advantage of Delta-Sigma ADCs is its insensitivity to imperfections and tolerances of the analog part of the ADC.
FIG. 1 illustrates a conventional error feedback (EFB) structure used in Delta-Sigma modulators. As shown in FIG. 1, an input signal X is received at a summer 102, and is inputted to a quantizer 104. The quantizer 104 outputs an output signal Y, which is also fed back to a second summer 106, together with the signal from the first summer 102. The second summer 106 outputs an error signal e, which is inputted into a filter 108 having a transfer function H1. The output of filter 108 is then fed back to the first summer 102. The transfer function of the output is given by:Y(z)=X(z)+[1−H1(z)]*E(z)  (Eq. 1)where H1(z) is the filter 108 transfer function, and Y, X and E are the z-transforms of the output y, the input x, and the quantization error e of the modulator. As shown in Eq. 1, the noise transfer function of the error feedback modulator is 1−H1(z). To achieve second order noise shaping, the feedback filter transfer function can be selected as H1(z)=2z−1−z−2, which results in the second order noise shaping 1−H1(z)=(1−z−1)2. The transfer function H1 of filter 108 thus gives second order noise shaping of the error signal.
The error feedback modulator has a relatively low cost of hardware and low power consumption, and, therefore, has been widely used in the low-power applications, such as digital voice and audio. This error feedback modulator, however, is subject to overflow when the modulator is over-driven. In another words, when the input is close to or greater than the full-scale (Fs) of the input, the quantization error −e in FIG. 1 becomes unbounded, driving the modulator towards oscillation and instability. In other words, the structure shown in FIG. 1, as noted above, has a stability problem when the input X is close to full scale (Fs). This results in extremely poor signal-to-noise plus distortion ratio (SNDR). To prevent overflow, a limiter has to be used, as shown in FIG. 2 (see generally S. R. Norsworthy, R. Schier and G. C. Temes, “Delta-Sigma Data Converters: Theory, Design, and Simulations,” IEEE Press, New York, 1997; P. Naus et al., “A CMOS Stereo 16-bit D/A Converter for Digital Audio,” IEEE Trans. on Solid-State Circuits, pp. 390 –395, vol. 22, no. 3, June 1987).
The quantizer 104 digitizes an analog voltage into a number of levels. For example, a one-bit quantizer, for an input voltage that is greater than zero, outputs a +1. For an input that is less than zero, the one-bit quantizer outputs −1. An N level quantizer divides the full scale (typically between −Fs and +Fs) into N levels, and outputs a discrete value accordingly. For example, for a three level quantizer, with full scale ranging from −1 volt to +1 volt, the quantizer will output discrete values at −0.5 and +0.5.
The output of the quantizer 104 introduces a quantization error, which may be fairly large. Therefore, the filter 108 is necessary to shape the frequency response. The fewer levels of quantization, the greater the quantization error.
FIG. 2 illustrates a modification of the circuit of FIG. 1. The modification includes the addition of a limiter 202 in the feedback path. The conventional value for the limiter is typically full scale (Fs) voltage, in other words, the limiter 202 does not permit the voltage in that particular feedback path to go above full scale.
The limiter transfer characteristic is shown in FIG. 3. The output of the limiter is saturated to full-scale (Fs) when the input of the limiter exceeds the Fs digital codes. When the modulator is overdriven, the error −e is bounded since both inputs are bounded, therefore, the modulator can be bring back to its stability when the modulator input is back to the normal range.
With the addition of the limiter 202, the inputs to the summer 106 are bounded, thereby reducing instability and oscillation of the output Y. FIG. 3 shows the transfer function of a conventional limiter 202. As shown in FIG. 3, once the input reaches a certain value, normally Fs, the output is flat at Fs as well.
The instability of the structure such as that shown in FIG. 1 when the input X approaches full scale is easily seen at the output Y, which does not reflect the input when the input is close to Fs. FIG. 4 shows a spectrum of the output Y, using a circuit of FIG. 2. As may be seen in FIG. 4, with an input of 2 KHz, strong harmonics are observed at 6 KHz, 10 KHz, 14 KHz, 18 KHz, etc. When a perfect sine wave is clamped or saturated into a trapezoid shape (i.e., “flat on the top”), its spectrum contains not only the component at the fundamental frequency (i.e., the original input frequency), but also significant 2nd order components (at twice the fundamental frequency), 3rd order components (three times the fundamental frequency) and other higher order harmonics. The spectrum shown in FIG. 4 contains components not only the fundamental frequency of 2 KHz, but also higher-order harmonics of 3rd order (at 6 KHz), 5th order (at 10 KHz), 7th order (at 14 KHz), etc. This is extremely undesirable, and represents distortion and nonlinearities.
However, the inventor has discovered that such a limiter 202 as described above is not optimal, because it saturates too early. This introduces unnecessary distortions and non-linearities into the output of the error feedback modulator.
Accordingly, there is a need in the art for a Delta-Sigma modulator with lower distortion.